Question #85ba3

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Answer 1 · 2016-08-31T18:10:32

The fundamental frequency of a streched string is given by the follwing formula.

$n=1/(2l)sqrt(T/m)$

Where

$l->"Length of the string"$

$T->"Tension of the string"$

$m->"Mass per unit length of the string"$

So T and m remaining constant

$nprop1/l$

let the frequency of the string is $n_1$ when its length is 20cm and its frequency is $n_2$ when its length is 21cm.
Si by the law of length

$n_1/n_2=21/20$

$Let" " n_1=21x Hzand n_2=20x Hz$

Let the frequency of tuning fork be $n_f$ It forms 10 beats with both length of the sonometer string.

So $n_1 >n_f>n_2$

So
$n_1-n_f=10=>21x-n_f=10......(1)$

Again

$n_f-n_1=10=>n_f-20x=10......(2)$

Adding (1) and (2) we get
$x=20$

Inserting the value of x in (2)

$n_f-20*20=10$

$n_f=410Hz$

$"Hence frequency of tuning fork"=410Hz$